Using lime wedges, moisten the rims of four margarita or cocktail glasses. Sprinkle salt on a plate; dip rims in salt. Set glasses aside.
Place tequila in a blender. Rinse kumquats; cut in half and remove seeds. Add to blender; cover and process until pureed. Strain, discarding skins and pulp.
Return puree to blender. Add the lime juice, ice and sugar; cover and process until blended. Pour into prepared glasses. Serve immediately.
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